Assignment:
The shaded region R, is bounded by the graph of y = x^2 and the line y = 4.
a) Find the area of R.
b) Find the volume of the solid generated by revolving R about the x-axis.
c) There exists a number k, k>4, such that when R is revolved about the line y = k, the resulting solid has the same volume as the solid in part b). Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.
Provide complete and step by step solution for the question and show calculations and use formulas.